The impulse response from a filter which is used for echo cancellation in telecommunication equipment shall as closely as possible immitate the impulse response of the transmission line in question. Included in the transmission line in such a case are two-wire to four-wire junctions, analogue-digital converters etc, which affect the impulse response. The latter generally has relatively long extension in time. It is therefore difficult to achieve a suitable impulse response with a filter which only has a finite impulse response. Such filters are called non-recursive filters or FIR filters (finite impulse response). For achieving a suitable impulse response, a filter for echo cancellation should comprise both a non-recursive part and a recursive part. Recursive filters are also called IIR filters (infinite impulse response).
There are known, reliable methods for updating adaptive FIR filters, i.e. adjusting the coefficients of such filters. They can be updated by minimizing the square of an error signal, which constitutes the difference between a so-called desired signal and the output signal of the filter. In such a case the desired signal may be a signal occurring on the receiver side in communication equipment where the filter is included. The square of the error signal can be minimized, e.g. according to the so-called LMS method (least mean square). The LMS method is described inter alia in the book: Widrow and Stearns, "Adaptive signal processing", pp 99-101.
Minimizing the square of an error signal according to the above is a so-called least square problem, due to the square of the error signal being a quadratic function of the filter coefficient values. This means that this square can be represented by a quadratic error surface, in an N-dimensional space where N is the number of coefficients, the optimum filter setting corresponding to the minimum point on this surface.
The corresponding square for an IIR filter is not represented by a quadratic error surface according to the above, however, and the error surface can have local minimum points instead. Known updating algorithms can fasten in such a local minimum point, resulting in that the optimum setting is never obtained.
Recursive filters can also be instable, as a result of that the poles in the Z transform of the transfer function can at least temporarily be moved outside the unit circle. For an IIR filter of the first degree, this means that the filter coefficient can be an amount greater than one, which makes the filter instable.
It is known to use a so-called "equation error" structure to avoid the problem with local minimii. In such a case two FIR filters are used, inter alia, of which one is connected to a transmitter side and the other to a receiver side in the same telecommunication equipment. An error signal is formed by the output signal of one filter being subtracted from the output signal of the other. The square of this error signal has a quadratic error surface, but a structure of this kind has the disadvantage that the minimized error signal does not represent the actual error. This is so, inter alia, when disturbances occur and when speech signals occur on the transmitter and receiver sides simultaneously. It has also been found difficult to adjust two filters which are connected in this way, due to the filters affecting each other. The equation error method is described, e.g. in the above-mentioned book "Adaptive signal processing", pp 250-253.